Illsley-Kemp, F., Keir, D., Bull, J. M., Ayele, A., Hammond, J., Kendall, J. M., Gallacher, R. J., Gernon, T., & Goitom, B. (2017). Local Earthquake Magnitude Scale and b‐Value for the Danakil Region of Northern Afar. Bulletin of the Seismological Society of America, 107(2), 521-531. https://doi.org/10.1785/0120150253

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This document is made available in accordance with publisher policies. Please cite only the published version using the reference above. Full terms of use are available: http://www.bristol.ac.uk/red/research-policy/pure/user-guides/ebr-terms/ Bulletin of the Seismological Society of America, Vol. 107, No. 2, pp. 521–531, April 2017, doi: 10.1785/0120150253 Ⓔ Local Earthquake Magnitude Scale and b-Value for the Danakil Region of Northern Afar by Finnigan Illsley-Kemp, Derek Keir,* Jonathan M. Bull, Atalay Ayele, James O. S. Hammond, J.-Michael Kendall, Ryan J. Gallacher, Thomas Gernon, and Berhe Goitom

Abstract The Danakil region of northern Afar is an area of ongoing seismic and volcanic activity caused by the final stages of continental breakup. To improve the quantification of seismicity, we developed a calibrated local earthquake magnitude scale. The accurate calculation of earthquake magnitudes allows the estimation of b-values and maximum magnitudes, both of which are essential for seismic-hazard analysis. Earthquake data collected between February 2011 and February 2013 on 11 three-component broadband seismometers were analyzed. A total of 4275 earthquakes were recorded over hypocentral distances ranging from 0 to 400 km. A total of 32,904 zero-to-peak amplitude measurements (A) were measured on the seismometer’s horizontal components and were incorporated into a direct linear inversion that M solved for all individual local earthquake magnitudes ( L), 22 station correction fac- C n K M ˆ A†− tors ( ), and 2 distance-dependent factors ( , ) in the equation L log log A0†‡C. The resultant distance correction term is given by − log A0†ˆ 1:274336 log r=17† − 0:000273 r − 17†‡2. This distance correction term suggests that attenuation in the upper and mid-crust of northern Afar is relatively high, con- sistent with the presence of magmatic intrusions and partial melt. In contrast, attenu- ation in the lower crust and uppermost mantle is anomalously low, interpreted to be caused by a high melt fraction causing attenuation to occur outside the seismic fre- M quency band. The calculated station corrections serve to reduce the L residuals sig- nificantly but do not show a correlation with regional geology. The cumulative seismicity rate produces a b-value of 0:9  0:06, which is higher than most regions of continental rifting yet lower than values recorded at midocean ridges, further sup- porting the hypothesis that northern Afar is transitioning to seafloor spreading.

Electronic Supplement: List of all local earthquakes used in the study with calculated local magnitudes and associated magnitude error.

Introduction The Danakil region, in northern Afar, is one of the few analysis, in particular when estimating b-values and maximum areas in the world where the transition from continental rifting magnitudes. Accurate local magnitudes are also essential for to seafloor spreading is exposed subaerially. The region is seis- studies that attempt to understand the geological processes oc- mically active and encompasses at least 24 active volcanic curring in locations such as northern Afar, for example, stress centers. The Ethiopian plateau, to the west of the Danakil de- accumulation and amount of strain by faulting. pression, supports a significant population. Given its proximity Seismic energy will attenuate at varying rates depending to the western border fault of Afar, the town of Mekele faces a on factors such as temperature, composition, and fluid high level of seismic risk and experienced a swarm of earth- content of the crust as well as partial melt and magmatic in- quakes in 2002 (Ayele et al.,2007). The accurate calculation trusions (Schlotterbeck and Abers, 2001; Carletti and Gas- of local magnitudes is a key component of seismic-hazard perini, 2003; Keir et al., 2006; Wang et al., 2009). This rate of attenuation is characterized by an attenuation curve. *Also at the Dipartimento di Scienze della Terra, Università degli Studi di The use of an inappropriate attenuation curve will result in Firenze, Florence, Italy. errors when assigning local magnitude values to earthquakes.

521 522 F. Illsley-Kemp, D. Keir, J. M. Bull, A. Ayele, J. O. S. Hammond, J.-M. Kendall, R. J. Gallacher, T. Gernon, and B. Goitom

Figure 1. The seismic network deployed for this study. The network was in place between February 2011 and February 2013. Stations marked with asterisks had one or more faulty horizontal components and so were not used for calculating magnitudes. The region contains the Erta-Ale volcanic segment (EAVS), the Dabbahu volcanic segment (DVS), (NVS), the Amarta-Barawli volcanic complex (ABVS), volcano (AV), and Alayta volcano Figure 2. Locations and respective magnitudes of the 4275 (ALV). Topography data were taken from National Aeronautics and earthquakes recorded in the two years between February 2011 Space Administration (NASA)’s Shuttle Radar Topography Mission. and February 2013. All earthquakes have a minimum of four phases recorded on a minimum of three stations. The black box outlines For two years, from 2011 to 2013, a seismic network was those earthquakes associated with the eruption of Nabro volcano. 260 150 deployed over an area covering × km (Figs. 1 ∼20 = and 2). The goal of this study is to use the seismic data re- mm yr in the south (13° N), with the extension – corded by 11 broadband seismometers to quantify seismic directed east-northeast west-southwest (McClusky et al., activity including improved estimation of local magnitudes 2010). The crust thins dramatically in the Danakil depres- ∼27 (M ). To do this, we invert maximum body-wave amplitude sion from km thickness in the rift to the south of the L <15 and hypocentral distance information to derive a region- depression to km beneath the depression (Makris and specific magnitude scale based on the definitions of Richter Ginzburg, 1987; Hammond et al.,2011). The crust is >40 (1935, 1958). km thick beneath the Ethiopian plateau (Hammond et al., 2011; Corti et al., 2015). The is an ∼200-km long 50–150-km Geological Setting wide basin that is mostly below sea level but currently sub- The Afar depression is a region that is in the late stages aerial (Fig. 1). Because of the low elevation, the surface sedi- of continental breakup and lies at the triple junction be- ments in the area largely consist of thick layers of evaporites tween the Gulf of Aden, the southern Red Sea, and the formed from repeated marine incursions (Barberi and Varet, Main Ethiopian rift (McKenzie and Davies, 1970; Mohr, 1970; Keir et al., 2013), most recently 32,000 years ago 1970). The initiation of rifting in Afar occurred between (Bonatti et al., 1971). The depression also contains the 31 and 29 Ma (Hofmann et al., 1997; Ukstins et al., NNW–SSE-trending Erta-Ale volcanic segment (EAVS) and 2002), with initial extension thought to be accommodated seven active volcanoes (Barberi and Varet, 1970; Nobile by large-scale border faults (Wolfenden et al., 2005). In et al., 2012; Fig. 1). The volcanic range is the focus for most northern Afar, strain localized to north-northwest–south- of the magmatic activity in the region and is responsible for southeast (NNW–SSE)-trending 10–30-km-wide 60–100- the majority of Quaternary to recent in Afar (Bastow km-long axial volcanic segments between 25 and 20 Ma and Keir, 2011). It is also thought to mark the boundary of (Hayward and Ebinger, 1996; Wolfenden et al., 2005). the Danakil microplate to the east (Eagles et al., 2002). Geo- Extension rates vary across the Danakil region, with exten- detic observations of Gada-Ale, Dallol, and Alu-Dalafilla sion of ∼7 mm=yr in the northernmost area (15° N) and volcanoes in the Erta-Ale range have been successfully mod- Local Earthquake Magnitude Scale and b-Value for the Danakil Region of Northern Afar 523

0 100 200 300 400 500 eled as fluxes of magma in upper-crustal reservoirs and in- 4000 trusions (Amelung et al., 2000; Field et al., 2012; Nobile Frequency et al., 2012; Pagli et al., 2012). Density 2000 In addition to the Erta-Ale volcanic range, there are a suite of other active volcanoes in the region (Fig. 1). At the southern 4000 2000 edge of the Danakil depression, there are the Amarta-Barawli 6 6 volcanic complex (ABVS), Afdera volcano (AV), and Alayta volcano (ALV) (Barberi and Varet, 1970). To the south of the 5 5 Danakil depression in central west Afar, the rift axis steps en ) echelon to the southwest into the Dabbahu segment (DVS), 4 4 L M which underwent a major dike intrusion episode during 2005– 2010 (Wright et al., 2006; Ebinger et al.,2008; Barnie et al., 3 3 2015). Nabro volcano (NVS), which erupted in June 2011, 2 2 is on the eastern margin of the Danakil depression near the Magnitude ( Eritrean–Ethiopian border (Hamlyn et al., 2014; Goitom et al., 2015; Fig. 1). 1 1 A variety of geophysical studies have shown that exten- sion in Afar and the Main Ethiopian rift is accommodated by 0 0 a combination of magmatic intrusion and lithospheric thin- 0 100 200 300 400 500 Hypocentral Distance (km) ning (e.g., Bastow and Keir, 2011). There is extensive evi- dence, from Interferometric Synthetic Aperture Radar, Figure 3. Magnitudes and hypocentral distances for the hori- magnetics, receiver functions, magnetotellurics, and seismic zontal components for all stations. Magnitudes are calculated using anisotropy for the presence of dikes and sills in the crust the magnitude scale for the Danakil region. south of 13° N in Afar (Wright et al., 2006; Keir et al., 2011; Bridges et al., 2012; Desissa et al., 2013; Hammond, 2014). 3ESPCD instruments and three Güralp CMG-6TD instruments Furthermore, a study into 40 years of seismicity in Afar by recorded continuous data at 50 Hz. A total of 4275 earthquakes Hofstetter and Beyth (2003) found that >50% of the geo- were recorded across the network during the experiment and detic moment, as predicted by plate separation rates, is taken were located with HYPO2000 (Klein, 2002). We used a 1D up aseismically. Along with a larger body of work, these re- velocity model based on a seismic refraction survey from the sults show that magmatic processes play an important role in area (Makris and Ginzburg, 1987). Accounting for instrument continental breakup (Calais et al., 2008; Thybo and Nielsen, faults, a total of 11 seismometers were used to calculate the 2009). North of 13° N, in the Danakil depression, extensive local magnitude scale. The velocity seismograms were con- crustal thinning is observed (Makris and Ginzburg, 1987; volved with the standard Wood–Anderson response, with a Hammond et al., 2011). This suggests that ductile stretching Wood–Anderson gain of 2800, to produce Wood–Anderson and thinning of the crust may also play an important role in displacement seismograms (Anderson and Wood, 1925; Kana- the accommodation of extension. mori and Jennings, 1978). The maximum peak-to-peak ampli- Many studies have attempted to investigate the thermo- tude on both the east–west and the north–south components of chemical state of the mantle beneath Afar. Seismic tomogra- each station was measured, in millimeters, for each event. The phy by Bastow et al. (2008) finds a broad low seismic-velocity final dataset consisted of 32,904 amplitude measurements with structure beneath the Main Ethiopian rift that extends to hypocentral distances ranging from 0 to 420 km (Fig. 3). depths of >400 km. Tomographic studies in northern Afar also show a region of low seismic velocity from 50 to 400 km Method depth, which is interpreted as a region of elevated tempera- ture and partial melt (Hammond et al., 2013; Stork et al., M The definition of local magnitude L is given by 2013; Civiero et al., 2015). This interpretation is further cor- Richter (1935, 1958): roborated by modeling geochemical data that suggest an M ˆ A† − A †‡C; † elevated mantle temperature of 1450° C (Ferguson et al., EQ-TARGET;temp:intralink-;df1;313;196 L log log 0 1 2013; Armitage et al., 2015). The elevated mantle tempera- ture will promote partial melting, even at relatively low rates in which A is the maximum zero-to-peak amplitude on the hori- of extension. zontal seismogram, log A0† is a distance correction term that is calculated empirically, and C is a correction term for each com- Data ponent of each station that is also calculated empirically. Richter originally defined the local magnitude scale M The seismic network comprised 16 broadband seismom- such that an earthquake of L 3 would cause a 1 mm eters that were operational for two years between February deflection on a standard horizontal Wood–Anderson seismo- 2011 and February 2013 (Fig. 1). Thirteen Güralp CMG- graph at a distance of 100 km from the hypocenter. Hutton 524 F. Illsley-Kemp, D. Keir, J. M. Bull, A. Ayele, J. O. S. Hammond, J.-M. Kendall, R. J. Gallacher, T. Gernon, and B. Goitom and Boore (1987) observed that Richter’s scale tended to (Keir et al., 2006). Our approach differs from many previous underestimate magnitudes at stations close to the hypocenter studies that have used an iterative technique (Langston et al., and overestimate for more distant stations. To counter this 1998; Baumbach et al., 2003). The direct inversion method is problem, they developed a method to calculate how attenu- computationally much faster and has been tested by Pujol ation rates vary over increasing hypocentral distances, which (2003) on data from Tanzania that was previously analyzed us- yields an attenuation curve for specific regions. This allows ing the iterative technique (Langston et al., 1998). The method for the magnitude scale to be normalized at a closer distance, used in this study has been tested on data from the Main Ethio- thus minimizing geographical variations in wave propaga- pian rift and yielded identical results to those produced by Keir M tion. They now define an L 3 earthquake as causing a et al. (2006). 10 mm deflection on a Wood–Anderson seismograph at a distance of 17 km from the hypocenter. The distance correc- tion term is defined as Results The inversion produced an equation for the distance cor- − A †ˆn r=17†‡K r − 17†‡2; † EQ-TARGET;temp:intralink-;df2;55;589 log 0 log 2 rection term log A0† for the Danakil region using a 17 km normalization in which n and K are constants to be calculated and relate to geometrical spreading and attenuation of seismic waves, − A †ˆ1:274336 r=17† − 0:0002731 r − 17†‡2: respectively, and r is the hypocentral distance in kilometers. EQ-TARGET;temp:intralink-;df5;313;557 log 0 log Combining equations (1) and (2), the observed ampli- 5† tude Aijk for each component of each station for each event can be written as Attenuation rates for the Danakil region (Fig. 4) are very sim- ilar to that of the Main Ethiopian rift for hypocentral distan- A †‡2 ˆ −n r =17† − K r − 17†‡M − C ; EQ-TARGET;temp:intralink-;df3;55;484 log ijk log ij ij L i† jk ces up to ∼70 km. For larger distances, the attenuation is 3† significantly lower than in the Main Ethiopian rift (Keir et al., 2006). The curve also shows that the attenuation rate in in which indexes i, j, and k represent events, stations, and the Danakil region is significantly higher than in Tanzania components, respectively. It is now possible to invert for (Langston et al., 1998). n K M C the unknowns , , L, and . Each station has two cor- The effect that the newly derived attenuation curve has rection terms associated with the north–south and east–west on magnitude estimates is shown in Figure 5. We show the horizontal components. The set of equations includes a con- magnitude residuals with increasing hypocentral distance straint that all station corrections sum to zero. The set of when using the magnitude scale for the Danakil region, equations (3) can be combined into a matrix form, shown the Main Ethiopian rift (Keir et al., 2006), and Tanzania in equation (4), which represents a dot product equation (Langston et al., 1998). Magnitude residuals calculated with d ˆ m · A and is a system of Ne ‡ 2Ns ‡ 2 unknowns, the new Danakil magnitude scale display no bias with hypo- in which Ne and Ns are the number of events and stations, central distance, and hence an average residual of near zero at respectively. The data from Danakil include 4275 events all hypocentral distances. In contrast, the Main Ethiopian rift recorded on 11 stations, producing a matrix with dimen- scale overestimates magnitudes with increasing hypocentral sions of 32;904 × 4299, with 4299 unknowns to be solved. distance, and the Tanzanian scale underestimates magni- Then, we solve equation (4) with a least-squares criterion tudes, as shown by the respective gradients of the residual and produce an optimal solution averages in Figure 5. The average variance of the residuals

EQ-TARGET;temp:intralink-;df4;55;230 0 1 n B C 0 1 B K C 0 1 log A111†‡2 B C log r11=17† r11 − 17† 10 010 0 B M C B C B L 1† C B C B log A112†‡2 C B C B log r11=17† r11 − 17† 10 001 0C B C B M C B C B C B L 2† C B C B . C B C B ...... C B . C B . C B ...... C B C B . C B C B A †‡2 C ˆ B C:B r =17† r − 17† 10 000 1C † B log 1Ns2 C B C B log 1Ns 1Ns C 4 B C BM C B C B A †‡2 C B L Ne† C B r =17† r − 17† 01 000 1C B log 211 C B C B log 21 21 C B C B C11 C B C B . C B C B ...... C @ . A B C @ ...... A B C12 C A †‡2 B . C r =17† r − 17† 00 100 1 log NeNs2 B C log NeNs NeNs @ . A C Ns2 Local Earthquake Magnitude Scale and b-Value for the Danakil Region of Northern Afar 525

Figure 4. Comparison of attenuation curves for the Danakil region (this study), the Main Ethiopian rift (Keir et al., 2006), Tan- zania (Langston et al., 1998), and southern California (Richter, 1958; Hutton and Boore, 1987). The attenuation rate in Danakil is significantly lower than that for the Main Ethiopian rift for hy- pocentral distances >70 km.

M for the Danakil magnitude scale is L 0.2; therefore the aver- M  0:2 age error in magnitude calculation is given as L . Individual magnitude errors for each event are listed in Ⓔ Tables S1 and S2, available in the electronic supplement to this article. To test whether the error in magnitude is de- pendent on magnitude value, we plot box plots of error val- ues for events grouped at 0.5 magnitude intervals (Fig. 6). This clearly shows that magnitude error is stable for the full range of magnitudes in this study. As a further test of the Figure 5. Magnitude residuals calculated for all events using magnitude scale, we compare Global Centroid Moment Ten- three different scales; the newly derived magnitude scale for (a) Da- M sor moment magnitudes ( w) from the Danakil region with nakil, (b) the Main Ethiopian rift magnitude scale (Keir et al., 2006), local magnitude values calculated with the derived magni- and (c) the Tanzania magnitude scale (Langston et al., 1998). The tude scale (Table 1). The listed events are assumed to be rep- Danakil magnitude scale minimizes residuals at all hypocentral dis- resentative, and worldwide comparisons of M and M find tances, whereas the Main Ethiopian rift scale and the Tanzania scale w L overestimate and underestimate magnitudes, respectively. the two scales to be, on average, consistent for shallow earth- quakes (<33 km; Kanamori, 1983).

there is no obvious link between regional geology and sta- Station Corrections tion correction. It is therefore most likely that station cor- The set of equation (4) includes a station correction term rection values are dependent on very local effects, such as Cjk for each component of each station. There is also a con- near-surface geology and the level of coupling between the dition included that all station corrections sum to zero. The seismometer and the soil. station corrections calculated for the east–west components Magnitude residuals, the magnitude calculated at a single M −0:25 – range from L 0.48 to units, and the north south- station minus the average magnitude, were calculated at all M −0:39 – – component corrections range from L 0.42 to units stations for both the north south and east west components (Fig. 7). Most stations have very similar station correction with and without station corrections (Fig. 8). Magnitude resid- values for the north–south and east–west components. uals calculated without station corrections have an average M − 1:3 10−2 Through examining the distribution of station corrections, of almost zero ( L × ) and a variance of 0.096. 526 F. Illsley-Kemp, D. Keir, J. M. Bull, A. Ayele, J. O. S. Hammond, J.-M. Kendall, R. J. Gallacher, T. Gernon, and B. Goitom

California (Hutton and Boore, 1987; Keir et al., 2006). High attenuation in southern California is explained by high geothermal gradients beneath the San Gabriel Mountains (Schlotterbeck and Abers, 2001). In the Main Ethiopian rift, the high rate of attenuation is ascribed to the presence of magmatic intrusions and partial melt within the crust (Keir et al., 2006). The Danakil region has an abundance of active volcanism and a thinned crust that suggests the presence of partial melt and high geothermal gradients. These conditions can explain the high level of attenuation at hypocentral dis- tances less than 100 km. The attenuation rate in Danakil is significantly lower than that in the Main Ethiopian rift at hypocentral distances Figure 6. Box plot of magnitude error versus magnitude, of over 100 km. Ray paths for earthquakes with hypocentral M binned in L 0.5 intervals. Box height represents the interquartile distances of over 100 and 150 km are shown in Figure 9. The range, and whiskers represent extreme values that are within 1.5 rays at these hypocentral distances predominantly traverse interquartile range. Magnitude errors are clearly shown to be stable from the Danakil depression in the north to the Dabbahu seg- for the reported magnitude range. ment in the south. We then calculated 2D travel-time curves using MacRay (Luetgert, 1992) and a velocity model based Magnitude residuals calculated with station corrections included on the seismic refraction survey by Makris and Ginzburg M − 3:3 10−8 have an average of very nearly zero ( L × )anda (1987), the results of which are shown in Figure 10. Earth- variance of 0.042. This shows that including the calculated quakes at these large hypocentral distances are sampling the station corrections brings the average residual closer to zero lower crust and uppermost mantle at a maximum depth of and reduces the variance by >64%. ∼45 km; therefore the low attenuation observed for the Da- nakil region is originating from these depths. A low attenu- ation rate could be consistent with a paucity of partial melt. Discussion However, previous geophysical work including high conduc- We compare the attenuation curve derived for the Dana- tivity in magnetotelluric data and high VP=VS of >2 imaged kil region with those from other regions worldwide (Fig. 4). by receiver functions strongly suggest that there is a large Attenuation is significantly higher in the Danakil region than amount of melt present in the lower crust and uppermost in Tanzania for all hypocentral distances greater than 50 km mantle (Hammond et al., 2011; Desissa et al., 2013). (Langston et al., 1998). The two regions are geologically It is therefore unlikely that low attenuation is caused by very different; Tanzania is a region of early-stage nonvol- low-melt fractions. Seismic attenuation in the upper mantle is canic continental rifting of Archaean cratonic lithosphere. thought to occur through two potential mechanisms: grain Archaean cratons generally consist of thick crystalline rock boundary sliding (Faul et al., 2004) and melt squirt (Mavko with very low geothermal gradients, both of which promote and Nur, 1975; O’Connell and Budiansky, 1977). Grain low seismic attenuation. The observed difference in seismic boundary sliding has been shown to cause a broad absorption attenuation can therefore be explained by the presence of the peak in the seismic frequency band and so cannot explain the Tanzanian craton. low attenuation that we observe (Faul et al., 2004). Ham- Our new attenuation curve shows that at hypocentral dis- mond and Humphreys (2000) modeled the effect that melt tances of less than 100 km, the attenuation in Danakil is very squirt has on attenuation in the upper mantle with melt per- similar to that in the Main Ethiopian rift and in southern centages ranging from 0% to 3%. They demonstrate that as

Table 1

A Comparison between Independently Calculated Moment Magnitudes (Mw) M and Local Magnitudes ( L)

† Date (yyyy/mm/dd) and Time (hh:mm:ss) Moment Magnitude Mw* Local Magnitude ML Depth (km) 2011/12/06 15:37:04 5.1 5.2 12 2011/12/06 19:21:50 5 5 1 2011/12/06 20:32:40 5.6 5.5 1 2011/12/06 21:03:23 5.4 5.7 2 2011/17/06 09:16:12 5.6 5.8 1

The events occurring on 12 June 2011 are associated with the eruption of Nabro volcano. *Moment magnitude calculated by Global Centroid Moment Tensor and U.S. Geological Survey. †Local magnitude calculated with local magnitude scale derived from this study. Local Earthquake Magnitude Scale and b-Value for the Danakil Region of Northern Afar 527

Figure 7. Variation of station corrections across the network. (a) North–south-component corrections. (b) East–west-component cor- rections. There is no clear correlation between regional geology and station correction. The corrections are therefore likely controlled by very local geology and site-specific variables. melt percentage increases, melt pockets become more inter- curs toward higher frequencies and away from the seismic connected and melt squirt can occur at a faster rate. This has frequency band. This interpretation of melt squirt causing the effect of pushing the frequency at which attenuation oc- low attenuation in the seismic frequency band has also been observed at the East Pacific Rise (Yang et al., 2007). We sug- gest that the low attenuation observed in the uppermost man- tle of Danakil can therefore be explained by a high melt fraction undergoing melt squirt. We used the new magnitude scale for the Danakil region to investigate the seismicity that occurred in the region be- tween February 2011 and February 2013. Figure 11 shows the Gutenberg–Richter distribution of log of the cumulative M number of earthquakes of magnitude L or greater (Guten- berg and Richter, 1956). The time period of the study fea- tured the eruption and associated seismic swarm of the Nabro volcano (Hamlyn et al., 2014; Goitom et al., 2015). Eruptions at caldera systems, such as Nabro, are extremely rare, and this was the first recorded eruption of the Nabro volcano. Because of the infrequent nature of the eruption, inclusion of the associated seismicity would bias the Guten- berg–Richter distribution. The events associated with the Nabro eruption have therefore been removed, based on their location at the volcano (latitude 13.1°–13.6°; longitude 41.5°–41.9°; Fig. 2). We estimate the magnitude of complete- Figure 8. (a) Magnitude residuals calculated with station cor- ness by initially using the maximum curvature method rections. (b) Magnitude residuals calculated without station correc- (Wiemer and Wyss, 2000), which corresponds to the magni- tions. Magnitude residuals calculated with station corrections sum to nearly zero, and the variance (0.042) has been reduced by tude bin with the highest event frequency. In our data this is M >64% when compared with the variance without station corrections L 1.8 (Fig. 11). However, Woessner and Wiemer (2005) (0.096). report that the maximum curvature method tends to under- 528 F. Illsley-Kemp, D. Keir, J. M. Bull, A. Ayele, J. O. S. Hammond, J.-M. Kendall, R. J. Gallacher, T. Gernon, and B. Goitom

Figure 10. (a) Travel-time curves for an earthquake occurring in the north of the Danakil depression. The S waves sample the uppermost mantle at hypocentral distances >100 km, reaching depths of up to 40 km. (b) Travel-time curves for an earthquake occurring in the south of the study area. The S waves sample the uppermost mantle at hypocentral distances >125 km, reaching depths of up to 45 km. Layer P-wave velocities are given in km=s, taken from Makris and Ginzburg (1987).

calculated an error of 0:06 by performing a bootstrap analysis following the method of Pickering et al. (1995). Including the events associated with the Nabro eruption in the b-value calculation reduces it to 0:8  0:04. This is un- surprising given the number of large-magnitude events that occurred during the eruption. It is important to note that b-values have been observed to change significantly over small distances and through time, particularly in areas of vol- canic activity (Wyss and McNutt, 1998; Barton et al., 1999; Wyss et al., 2001). The Danakil region has a higher b-value than most other areas in the East African rift. South , Tanzania, and Kenya, which are all regions of continental rifting, have b- values that range from 0.7 to 0.9 (Tongue et al., 1992; Ayele and Kulhanek, 1997; Langston et al., 1998). The Danakil re- gion b-value is also significantly higher than that in other continental rift systems, such as the Rio Grande and Eger rifts, both of which exhibit b-values of 0.8 (Ibs-von Seht et al., 2008). In these regions, rifting is less developed and also less magmatically accommodated. A lack of magmatic activity Figure 9. The ray paths for earthquakes with hypocentral dis- during rifting allows greater stresses to accumulate in the tances over (a) 100 and (b) 150 km. The ray paths predominantly crust, facilitating larger earthquakes and a lower b-value. traverse the Danakil depression and Dabbahu segment region. The b-value for Danakil is lower than values recorded at midocean ridges. At the Mid-Atlantic ridge, b-values have estimate the magnitude of completeness by 0.1–0.2 magni- been observed to vary, but they are consistently above 1 and tude units, and we therefore estimate a magnitude of com- can reach values of up to 1.5 (Kong et al., 1992; Barclay et al., M b pleteness of L 2.0. A -value of 0.9 was calculated 2001; Tilmann et al., 2004). Wilcock et al. (2002) performed a using the maximum-likelihood calculation (Aki, 1965). We microearthquake study on the Endeavour segment of the Juan Local Earthquake Magnitude Scale and b-Value for the Danakil Region of Northern Afar 529

in which r is the hypocentral distance from station to earth- quake. This equation and the corresponding attenuation curve show that the attenuation rate of seismic energy in Danakil is relatively high in the crust, consistent with the presence of magmatic intrusions and melt. The relatively low attenuation observed at greater depths could indicate a low melt percent- age, inconsistent with independent geophysical data. We therefore suggest that the low attenuation rate is due to a sufficiently high melt fraction in the upper mantle beneath Da- nakil undergoing melt squirt and causing the seismic attenu- ation to occur outside the seismic frequency band. We used the seismicity in Danakil to produce a Guten- berg–Richter relationship. The catalog is complete above M b 0:9  0:06 L 2.0 and the calculated -value is given as . Our b-value is consistent with the area transitioning to sea- floor spreading. Our improved magnitude scale and seismic- ity rate are critical for better quantification of seismic hazard. These results will also help quantify the distribution and amount of seismic strain. Figure 11. Analysis of earthquake magnitude distribution of earthquakes in the Danakil region, excluding those associated with the eruption of Nabro on 12 June 2011. (Left axis) Gutenberg– Data and Resources Richter distribution in which log N† represents the log of the cu- M mulative number of earthquakes of magnitude L or greater. (Right Seismograms used in this study were collected as part axis) Number of events represents the frequency of events in each of the Afar0911 experiment using Seismic Equipment M magnitude bin. The magnitude of completeness ( L 2.0) is calcu- Infrastructure in the UK (SEIS-UK) instruments. We pro- lated using the maximum curvature method (Wiemer and Wyss, 2000). We calculate the b-value using the maximum-likelihood vide the catalog of earthquakes used in this study in the method. The calculated b-value suggests that geodetic strain is pri- electronic supplement to this article. Plots were made using marily released through swarms of low-magnitude earthquakes, the Generic Mapping Tools v. 4.5.8 (www.soest.hawaii. rather than large-scale faulting. edu/gmt, last accessed September 2015; Wessel and Smith, 1998). de Fuca ridge and recorded a b-value of 1.06. These b-values Acknowledgments suggest that seismic energy at ocean ridges is primarily re- We thank Seismic Equipment Infrastructure in the UK (SEIS-UK) for leased through swarms of relatively low-magnitude earth- use of the instruments and their computing facilities. The facilities of SEIS- quakes. The observation that the b-value for the Danakil UK are supported by the Natural Environment Research Council (NERC) region lies between those found at midocean ridges and at re- under Agreement R8/H10/64. F. I.-K. is funded through NERC studentship gions of continental rifting suggests that the Danakil region is NE/L002531/1 and a grant to Graduate School of the National Oceanogra- phy Centre of Southampton (GSNOCS) from Roy Franklin O.B.E. D. K. at the transition from continental rifting to seafloor spreading. is supported by NERC Grant Number NE/L013932. Funding for fieldwork The calculation of accurate local earthquake magnitudes is from BHP Billiton. We also acknowledge assistance from Addis Ababa is essential for estimating maximum magnitudes and for bet- University and the Afar National Regional State Government. We would like ter quantification of time–space variations in seismicity to thank Yavor Kamer and an anonymous reviewer for constructive reviews b-values. 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